Some Remarks on the fcc-fct Phase Transformation in InTl Alloys

Zimmer and collaborators have recently proposed an alternative approach to Landau's for phase transformations, in which they replace the energy expression in terms of polynomials, a stiff family of functions, with one in terms of more flexible functions, for instance certain splines. One of the arguments in favor of this more flexible choice is the inability of an energy proposed earlier by Ericksen and James to fit reasonably well all the elasticities of an InTl alloy, in particular the wide difference in the measured (L) over cap (44) and (L) over cap (66) elasticities of the InTl martensite. While the proposal of Zimmer is theoretically very interesting and fit for numerical applications, and shows potential for modelling materials with complex internal structure, here I show that the pessimism about the standard Landau approach is indeed excessive as far as the weak points of the Ericksen-James energy are concerned. I propose a fourth-degree polynomial energy which extends the one of Ericksen and provides a fairly accurate fit of the equilibria as well as the elasticities for an In15.5\%Tl alloy; and perhaps also for different compositions in the InTl family. The starting point is the version of Ericksen's theory [5] given in [12].